Heat the butter in a large saucepot over medium heat. Add the curry powder and cook, stirring, until toasted, about 30 seconds. Add the garlic, carrot, celery, onion, 1/4 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until tender, about 8 minutes.
Add the broth and bring to a boil. Reduce the heat to a simmer and stir in the chicken and rice. Cook until the chicken is heated through. Remove from the heat and stir in the lime zest and juice and the cilantro; season with additional salt and pepper. Serve topped with fresh cilantro leaves.
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